In the modeling of multivariate extreme risks, the tail dependence and the heavy tailedness are the two key factors. Heavy tailedness are usually defined through the regular variation. Tail dependence can be modeled by copulas with the so-called tail order property. In this paper, we propose a new risk measure called the Joint Expected Shortfall (JES) as an alternative of quantifying extreme risks. The JES, which can be viewed as a consolidation of both Expected Shortfall (ES) and Marginal Expected Shortfall (MES) risk measures, has the desirable property of measuring risk by jointly capturing both tail dependence and heavy tailedness. The asymptotic analysis of JES is conducted to provide a simple and transparent way of studying the interplay between tail dependence and heavy tailedness. Various examples are presented to illuminate our results. In particular, risk measures such as ES and MES that ignore the joint effect of dependence and heavy tailedness may severely underestimate the underlying risk.

在多变量极端风险建模中，尾部依赖性和沉重的尾部性是两个关​​键因素。重尾通常通过规则变化来定义。尾巴的依赖关系可以通过具有所谓尾巴顺序属性的系词来建模。在本文中，我们提出了一种称为联合预期缺口（JES）的新风险度量，作为量化极端风险的替代方法。JES可以看作是预期不足（ES）和边际预期不足（MES）风险度量的合并，具有通过联合捕获尾部依赖和严重尾部来度量风险的理想属性。进行JES的渐近分析，以提供一种简单而透明的方法来研究尾部依赖和沉重尾部之间的相互作用。给出了各种示例以阐明我们的结果。